The aim of this paper is to investigate collective excitations and the damping rate in a multilayer structure consisting of three monolayer graphene sheets with inhomogeneous background dielectric at zero temperature within random-phase approximation. Numerical results show that one optical branch and two acoustic ones exist in the system. The lowest frequency branch disappears as touching single-particle excitation area boundary while two higher frequency branches continue in this region. Calculations also illustrate that the frequency of optical (acoustic) mode(s) decreases (increase) as interlayer separation increases. |